Fly boxes; storage boxes for bigger flies; then two jars. One jar gets flies to recycle beads and hooks. The other jar gets flies to give away.
At least once a year I'll replace flies with better ties. The old ones go to the jars.

That is what happens to us Phil, I have a stack of them but only ever carry 2 on me. You might try the species specific box approach, or the wet / dry way. I used to carry a streamer wallet and a small dry selection when fishing the states.

What I currently do is have 5 wheatley fly boxes and 2 cf design fly boxes. The CF designs get used for bass flies, they're deep and accommodate big poppers.

The 6" wheatleys are setup 1 for streamers, 1 for nymphs/wets/worms/eggs, 1 for dries, 1 for terrestrials and a 4" for tiny dries and nymphs on threaders. I usually end up with 3 or 4 boxes on the water. Sometimes I do mix a few patterns in each. But they're divided up for the most part.

Everything else goes into one of these from Plano:

It holds 4 separate plano boxes inside. Can easily grab the whole thing and throw it in the car.

I use various boxes & bags to both store & carry flies. I have 2 of the boxes that Dennis posted. They're my boat boxes. I use different size Plano/Flambeau boxes to keep my extra flies, several fly boxes for different types of flies that I'll carry, and a couple of the bags that are normally used for plastic baits. I use them for some bigger flies, and add some extra inserts so I have quite a few flies in a bag.

I don't have pictures of the bags, but do have some of the various boxes I use.

This is a Fox Box.

My 2 boat boxes. Same as the box Dennis posted.

Waterproof Fly Boxes.

Medium Plano/Flambeau box.

Large Plano/Flambeau.

Another Medium Plano/Flambeau box.

Flambeau box, polystyrene. Clear. I used these for display when I tied flies commercially. Don't like carrying them as this type plastic cracks easily, but they're great for storage.

These guys have it nailed. Adjustable storage boxes from Plano for me. I have one smaller Myran that I use to keep dries in. For day trips, I keep them at the house, but when going out for a few days, I usually take them with me and replenish as needed.